Three women, Jean, Irene and Winnie went on a shopping spree. 30% of Jean's spending was equal to ¹₅ of Irene's spending. Winnie's spending was  40% less than Irene's. If Irene spent $462 less, she would spend the same amount of money as Winnie.

1. Find the ratio of Jean's spending to Irene's to Winnie's.
2. How much did Winnie spend?

Jean	Irene	Winnie
2x5	3x5
	5x3	3x3
10 u	15 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Jean's spending is equal to ¹₅ of Irene's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Jean's spending = 15 of Irene's spending
310 of Jean's spending =1x35x3 of Irene's spending
310 of Jean's spending = 315 of Irene's spending

Jean : Irene
10 : 15
2 : 3

Winnie's spending in percent when compared to Irene's
= 100% - 40%
= 60%

Irene : Winnie
100 : 60
5 : 3

Irene's spending is the repeated identity.  Make Irene's spending the same.  LCM of 3 and 5 is 15.

Jean : Irene : Winnie
10 : 15 : 9

(b)

	Jean	Irene	Winnie
Before	10 u	15 u	9 u
Change		- 6 u
After	10 u	9 u	9 u

Additional amount that Irene would have to spend less to be the same as Winnie
= 15 u - 9 u
= 6 u

6 u = 462

1 u = 462 ÷ 6 = 77

Amount that Winnie spent
= 9 u
= 9 x 77
= $693 

Answer(s): (a) 10 : 15 : 9; (b) $693